🧮 algebra

1. **State the problem:** Solve the equation $$(2x + 5)^2 = (2x + 3)(2x - 1)$$ for $x$. 2. **Use the formula and expand both sides:**

1. We gaan een oefening over machten uitleggen. 2. Een macht is een manier om een getal meerdere keren met zichzelf te vermenigvuldigen. Bijvoorbeeld, $a^n$ betekent dat je het get

1. **State the problem:** We want to show that $$\frac{\sqrt{12}}{\sqrt{3}+2}$$ can be written in the form $$a + \sqrt{b}$$ where $$a$$ and $$b$$ are integers. 2. **Recall the form

1. **State the problem:** Simplify the expression $-\frac{8}{2}\left(-\frac{8}{7}\right)$.\n\n2. **Recall the rules:** Multiplication and division are performed from left to right.

1. **State the problem:** Simplify the expression $-6\left(\frac{4}{5}\right)$.\n\n2. **Recall the rule:** Multiplying a whole number by a fraction means multiplying the numerator

1. El primer problema del usuario es el número 61: Resolver la expresión $2m^2n + 6mn^2 + 8mns$. 2. Para resolver o simplificar esta expresión, buscamos factor común en todos los t

1. **State the problem:** Simplify the expression $\frac{-3}{4} \div \frac{-6}{7}$. 2. **Recall the division rule for fractions:** Dividing by a fraction is the same as multiplying

1. **State the problem:** Simplify the expression $24 \div \left(-\frac{3}{4}\right)$. 2. **Recall the division rule for fractions:** Dividing by a fraction is the same as multiply

1. **State the problem:** Simplify the expression $-12 \div \frac{6}{5}$. 2. **Recall the rule:** Dividing by a fraction is the same as multiplying by its reciprocal. So, $a \div \

1. The problem is unclear as given, but it appears to involve simplifying or solving an expression involving variables $x$ and $y$ and possibly powers or coefficients. 2. Since the

1. **State the problem:** Mark and Tracy's combined ages total 44 years. We need to find Mark's current age given a complex age relationship. 2. **Define variables:** Let $M$ = Mar

1. **Problem Statement:** Factor the trinomial 4x^2 + 16x + 12. 2. **Formula and Rules:** To factor a trinomial of the form $ax^2 + bx + c$, find two numbers that multiply to $ac$

1. **Problem:** Find all possible values of $b$ for which $7x^2 + bx + 3$ is factorable into linear factors with integer coefficients and constants. 2. **Formula and rules:** For a

1. El problema consiste en analizar y resolver las expresiones dadas para $h$ en función de $SA$ y $s$. 2. Las fórmulas son:

1. The problem states that $y$ is inversely proportional to $x$. This means the relationship can be written as: $$y = \frac{k}{x}$$

1. **State the problem:** Solve the equation $5a + b = 16$ for one variable in terms of the other. 2. **Choose a variable to solve for:** Let's solve for $b$ in terms of $a$.

1. **State the problem:** Solve a system of linear equations using the elimination method. 2. **Explain the elimination method:** The elimination method involves adding or subtract

1. **State the problem:** Solve the equation $$\frac{2}{7} (z - 10) = -3$$ for $z$. 2. **Use the distributive property and isolate $z$:** Multiply both sides by 7 to eliminate the

1. **State the problem:** Simplify and solve the expression $$2(x^2 + x - 4)^2 - 4 + \frac{1}{16}$$. 2. **Rewrite the expression:**

1. **State the problem:** Expand the expression $ (x+3)^4 $ into a standard polynomial form. 2. **Formula used:** Use the Binomial Theorem which states:

1. **Problem statement:** We are given two functions $P(x)$ and $Q(x)$ with specified end behaviors: - $P(x) \to -\infty$ as $x \to +\infty$ and $P(x) \to +\infty$ as $x \to -\inft